Scientific Program

Semi-plenary Lecture

Program -> Plenary and Semi-Plenary -> Mon.17:00.H 0104 title only | abstract | bio sketch

Monday, 17:00 - 17:50 h, H 0104


Katya Scheinberg
Using randomized models in black-box and derivative free optimization


Chair: Luís Nunes Vicente


Abstract:
All derivative free methods rely on sampling the objective function at one or more points at each iteration. Direct search methods (developed by Dennis, Torczon, Audet, Vicente and others) rely on sample sets of defined configuration, but different scales. Model-based DFO methods (developed by Powell, Conn, Scheinberg, Toint, Vicente, Wild and others) rely on building interpolation models using sample points in proximity of the current best iterate. Constructing and maintaining these sample sets has been one of the most essential issues in DFO. Many of the existing results have been summarized in a book by Conn, Scheinberg, Vicente, where all the sampling techniques considered for deterministic functions are deterministic ones.

We will discuss the new developments for using randomized sampled sets within the DFO framework. Randomized sample sets have many advantages over the deterministic sets. In particular, it is often easier to enforce "good" properties of the models with high probability, rather than the in the worst case. In addition, randomized sample sets can help automatically discover a good local low dimensional approximation to the high dimensional objective function. We will demonstrate how compressed sensing results can be used to show that reduced size random sample sets can provide full second order information under the assumption of the sparsity of the Hessian.

We will discuss new convergence theory developed for the randomized models where we can, for instance, show that as long as the models are "good" with probability more than 1/2 then our trust region framework is globally convergent with probability 1 under standard assumptions.

 

 

Program -> Plenary and Semi-Plenary -> Mon.17:00.H 0104 title only | abstract | bio sketch

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